Mr. Worley
2025 Oct 06
ABAC-BB-BAC-CA--BB-BB--BB-BAC-CA--CA-BAC---BB-BB--BB-BB---BB-BB--BB-BAC-CA--CA-BAC---CA-BAC--BB-BAC-CA----B B - B B -- B B - B A C - C A -- C A - B A C ---
BB- BB- - BB- BB- -- BB- BB- - BB- BAC- CA- - CA- BAC- -- CA- BAC- - BB- BAC- CA- ---
Imagine a turtle dragging a pen across an \((x,y)\) plane. If various characters (letters) in a string represent commands, we can see that L systems lead to fractal-like patterns.
A common set of commands:
So, using our example from the previous page, and starting pointing North (up)…
BB-BB--BB-BB---BB-BB--BB-BAC-CA--CA-BAC---CA-BAC--BB-BAC-CA----
Angle = 30°
Start = A
Rules:
A > A[+A][-A]B
B > [--B]A
Number of recursions = 7
Angle = 60°
Start = A
Rules:
A > -B+B+B+B+B+B
B > B[--CCA][-CCA]B
C > CC
Number of recursions = 7
Angle = 45°
Start = A
Rules:
A > [----AAB][--AAB][++AAB]AAB
B > [-C][+C][--C][++C][---C][+++C]
C > CAB
Number of recursions = 6
Angle = 72°
Start = A
Rules:
A > [-AAB][--AAB][+AAB][++AAB]AAB
B > [-C][+C][--C][++C]CA
C > CC
Number of recursions = 5
Angle = 60°
Start = a
Rules:
a > -B+B+B+B+B+B
B > BB[-CCa]
C > CC
Number of recursions = 9
Angle = 72°
Start = A
Rules:
A > B+B+B+B+B
B > [-CCA]BB
C > CC
Number of recursions = 9
Angle = 45°
Start = A
Rules:
A > +A-B-B[B]
B > -B+A+A[A]
Number of recursions = 8
Angle = 90°
Start = A
Rules:
A > AA[-A][+A]
Number of recursions = 8
Angle = 30°
Start = A
Rules:
A > AcbcA
b > [+A][-A][++A][--A][+++A][---A][++++A][----A][+++++A][-----A]
c > bAb
Number of recursions = 6
Angle = 30°
Start = AB
Rules:
A > B--B
B > AA+++AA
Number of recursions = 12
Angle = 30°
Start = x
Rules:
x > FFF[+FFF+FFF+FF+FF+F+Fx][-FFF-FFF-FF-FF-F-Fx]Fx
F > FFx
Number of recursions = 6
Angle = 45°
Start = A
Rules:
A > AB
B > A[++C][--C]
C > C[+C][-C]A
Number of recursions = 10
Angle = 25°
Start = -x
Rules:
x > F+[[x]-x]-F[-Fx]+x
F > FF
Number of recursions = 7
Angle = 90°
Start = b
Rules:
A > AA
b > AbA+AbA+AbA
Number of recursions = 9
Angle = 115°
Start = A
Rules:
A > A+A-A
Number of recursions = 11
Angle = 90°
Start = A
Rules:
A > A[+AA][-AA]B
B > ABA
Number of recursions = 7
Angle = 6°
Start = x
Rules:
x > FFF[+FF+FF+FF+F+Fx][-FF-FF-FF-F-Fx]FFFFFFFFFFFFFFx
F > FF
Number of recursions = 8
Angle = 60°
Start = A+++A+++.A+++A
Rules:
A > A[-A]A
Number of recursions = 8
Angle = 72°
Start = [A][+A][++A][-A][--A]
Rules:
A > X[-A][+A]AA
X > XX
Number of recursions = 7